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How so I say "hey can you pass my resume to recruiting/can you give me a summer associate job/help me out" to a partner during an informational phone call? I randomly reached out. Firm doesn't come to school.

Don't ask him/her directly, since you never want to make them uncomfortable. Try something along the lines of "Do you have any advice about how to search for positions in the field?" or "Are there any firms you'd recommend I approach about working in this field?"

Hm really? I've heard from some people that I should not be shy about that stuff. Anyone else care to chime in?

Ask general questions that build up to those things ("How do people typically get SA gigs?" and the like). If they open the door to those direct questions, feel free to raise it, but don't just spring it on them.